*DECK COSQF
SUBROUTINE COSQF (N, X, WSAVE)
C***BEGIN PROLOGUE COSQF
C***PURPOSE Compute the forward cosine transform with odd wave numbers.
C***LIBRARY SLATEC (FFTPACK)
C***CATEGORY J1A3
C***TYPE SINGLE PRECISION (COSQF-S)
C***KEYWORDS COSINE FOURIER TRANSFORM, FFTPACK
C***AUTHOR Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C Subroutine COSQF computes the fast Fourier transform of quarter
C wave data. That is, COSQF computes the coefficients in a cosine
C series representation with only odd wave numbers. The transform
C is defined below at Output Parameter X
C
C COSQF is the unnormalized inverse of COSQB since a call of COSQF
C followed by a call of COSQB will multiply the input sequence X
C by 4*N.
C
C The array WSAVE which is used by subroutine COSQF must be
C initialized by calling subroutine COSQI(N,WSAVE).
C
C
C Input Parameters
C
C N the length of the array X to be transformed. The method
C is most efficient when N is a product of small primes.
C
C X an array which contains the sequence to be transformed
C
C WSAVE a work array which must be dimensioned at least 3*N+15
C in the program that calls COSQF. The WSAVE array must be
C initialized by calling subroutine COSQI(N,WSAVE), and a
C different WSAVE array must be used for each different
C value of N. This initialization does not have to be
C repeated so long as N remains unchanged. Thus subsequent
C transforms can be obtained faster than the first.
C
C Output Parameters
C
C X For I=1,...,N
C
C X(I) = X(1) plus the sum from K=2 to K=N of
C
C 2*X(K)*COS((2*I-1)*(K-1)*PI/(2*N))
C
C A call of COSQF followed by a call of
C COSQB will multiply the sequence X by 4*N.
C Therefore COSQB is the unnormalized inverse
C of COSQF.
C
C WSAVE contains initialization calculations which must not
C be destroyed between calls of COSQF or COSQB.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations (G. Rodrigue, ed.), Academic Press,
C 1982, pp. 51-83.
C***ROUTINES CALLED COSQF1
C***REVISION HISTORY (YYMMDD)
C 790601 DATE WRITTEN
C 830401 Modified to use SLATEC library source file format.
C 860115 Modified by Ron Boisvert to adhere to Fortran 77 by
C (a) changing dummy array size declarations (1) to (*),
C (b) changing definition of variable SQRT2 by using
C FORTRAN intrinsic function SQRT instead of a DATA
C statement.
C 861211 REVISION DATE from Version 3.2
C 881128 Modified by Dick Valent to meet prologue standards.
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE COSQF
DIMENSION X(*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT COSQF
SQRT2 = SQRT(2.)
IF (N-2) 102,101,103
101 TSQX = SQRT2*X(2)
X(2) = X(1)-TSQX
X(1) = X(1)+TSQX
102 RETURN
103 CALL COSQF1 (N,X,WSAVE,WSAVE(N+1))
RETURN
END